A finite time flight altitude control method integrating flap direct force control

Abstract

The present application belongs to the field of aircraft flight control, and particularly relates to a kind of finite time flight height control method of integrated flap direct force control.The finite time flight height control method of integrated flap direct force control according to height control reference trajectory, establishes the linear dynamics model of the longitudinal channel of the controlled aircraft;According to the flight control target, a finite time domain linear quadratic optimal control problem is established, and the corresponding two-point boundary value problem is derived;Using finite-time iteration algorithm, the optimal flight state and control solution of flight height control are obtained;The optimal solution is applied to height control.The finite time flight height control method of integrated flap direct force control uses finite-time iteration to obtain optimal control instructions, and through parallel computing, efficient solution of height and heading position control instructions is realized, which has engineering practical value.

Description

Technical Field

[0001] This invention belongs to the field of aircraft flight control, specifically relating to a finite-time flight altitude control method based on integrated flap direct force control. Background Technology

[0002] Direct force control (DFC) is an advanced method for aircraft trajectory control. This method uses additional aerodynamic control surfaces, such as flaps, to directly alter the forces acting on the aircraft without changing its attitude, thereby rapidly changing its trajectory. DFC reduces the time lag between control and trajectory change, enabling the aircraft to quickly and accurately reach the desired position in the air. It improves attitude control and allows for efficient trajectory control while maintaining a relatively stable aircraft attitude, significantly enhancing maneuverability and agility. For certain mission scenarios requiring rapid adjustments to altitude and position within a limited time, flap-based DFC can improve the quality of such missions.

[0003] Linear quadratic optimal control is a widely used control method. It not only provides optimal control strategies for linear systems but also demonstrates good performance as an efficient approximate control method in nonlinear systems. However, for finite-time linear quadratic optimal control problems with a specified terminal state, the classic Riccati matrix differential equation solution method involves solving multiple matrix differential equations, making the solution process tedious and complex. Traditional target-based solutions suffer from high requirements for initial conditions, small convergence regions, long optimization iteration times, and even computational failures. Furthermore, in Hamiltonian dynamics systems derived from optimality conditions, the stability of costate variables and state variables are inversely related. When numerically solving Hamiltonian dynamics systems, system instability can lead to significant computational errors, often resulting in numerical solution failure.

[0004] Therefore, it is necessary to develop a finite-time flight altitude control method that integrates flap direct force control to address the problem of finite-time flight altitude control for aircraft. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to provide a finite-time flight altitude control method that integrates flap direct force control.

[0006] like Figure 1 As shown, the finite-time flight altitude control method based on integrated flap direct force control of the present invention includes the following steps:

[0007] S10. Based on the altitude control reference trajectory, establish a longitudinal channel linearized dynamic model of the controlled aircraft;

[0008] S20. Based on the flight control objective, establish a finite-time linear quadratic optimal control problem and derive the corresponding two-point boundary value problem;

[0009] S30. A finite-degree symplectic integral algorithm is used to solve the problem in parallel to obtain the optimal flight state and control solution for flight altitude control;

[0010] S40. Apply the optimal solution to aircraft altitude control.

[0011] Furthermore, the specific content of S10 is as follows:

[0012] Given an altitude control reference trajectory for the aircraft, the nonlinear motion equations of the aircraft are linearized and expanded near the reference trajectory. To achieve control of the aircraft's altitude and heading, altitude, heading, pitch rate, velocity amplitude, and longitudinal velocity are selected as state variables, and elevator, flaps, and engine throttle are used as control variables. The elevator provides pitch moment control, the flaps provide direct force control, and the engine throttle provides thrust control. The specific form of the established longitudinal channel state equations is as follows:

[0013] ;

[0014] in, For state variables, This refers to the altitude error of the aircraft relative to the reference trajectory. For heading and position error, For pitch angular velocity error, For velocity amplitude error, For pitch attitude angle error, For longitudinal velocity error, To control variables, For the change in the aircraft's elevator. Flange change amount To change the amount of throttle, yes 3D matrix yes 3D matrix State variables The first derivative with respect to time, This indicates the matrix transpose.

[0015] Furthermore, the specific content of S20 is as follows:

[0016] Based on the flight control objective, a finite-time linear quadratic optimal control problem is established. The dynamic transition process of the state variables during aircraft altitude control is adjusted using the weight matrix in the integral performance index. Regarding the values ​​of the terminal state variables, for state variables with specified terminal values, equality constraints are directly set in the optimal control problem; for state variables without specified terminal values, constraints are indirectly imposed using the final value performance index. Furthermore, based on optimal control theory, a two-point boundary value problem based on Hamiltonian dynamics is derived. The specific process is as follows:

[0017] ;

[0018] in, for forward A variable formed by elements for back A variable formed by elements and They are Wei and A positive definite symmetric matrix for A nonnegative definite symmetric matrix, and These are the given initial time and terminal time, respectively. Given an initial value, for Given the final value;

[0019] Based on optimal control theory, the two-point boundary value problem based on Hamiltonian dynamics is derived as follows:

[0020] ;

[0021] in, For state variables The corresponding costate variable, for back A variable formed by several elements.

[0022] Furthermore, the specific content of S30 is as follows:

[0023] For the two-point boundary value problem based on Hamiltonian dynamics systems, based on the principle of superposition of solutions to linear differential equations and combined with the initial conditions of state variables, and given a finite set of initial guesses for costate variables, a symplectic integral algorithm is used to solve the initial value problem in parallel within a given finite time domain. This yields the optimal flight state variable solution and costate variable solution that meet preset conditions. The corresponding optimal control solution is then calculated, leading to the elevator, flap, and engine throttle control commands for the aircraft, which are then applied to the aircraft's altitude and heading position control. The specific process is as follows:

[0024] Based on the principle of superposition of solutions to linear differential equations, combined with the initial conditions of the state variables... Given 7 sets of costate variables Initial guess: The symmetric integral algorithm is used in the time interval Parallel integration is used to solve the initial value problem; since the dynamic system consists of linear equations, the symplectic integration algorithm does not require solving implicit equations. The state variable and costate variable solutions are obtained directly through progression. For the Sinusoidal integration method, starting from the... Time step to the 1st The time step is calculated as follows:

[0025] ;

[0026] in, As a unit array, For discrete time steps, Representing the The time value of the time step. and The first Control variables, state variables, and costate variables at each time step. and The first State variables and costate variables at each time step;

[0027] The corresponding state variable solutions are obtained by parallel solving using the symplectic integral algorithm. With costate variable solution Then, the final solution for the state variables and the solution for the costate variables are:

[0028] ;

[0029] in, For the coefficients to be determined, satisfying Based on the terminal boundary conditions, the coefficients to be determined are:

[0030] ;

[0031] in, For variables At the terminal time The value of ; For variables At the terminal time The value of ;

[0032] Note: Initial guess The selection condition is: None exists. , making ;get Then, using the control solution and By considering the relationship between the aircraft's altitude and heading position, the optimal elevator, flap, and engine throttle control solutions are obtained.

[0033] The finite-time flight altitude control method based on integrated flap direct force control of the present invention can ensure the optimal control command by solving the problem in a finite number of iterations. This avoids the problems of the target shooting method, which has high requirements for initial value setting, small convergence domain, long optimization iteration time, and even possible calculation failure. By parallel computing, the solution efficiency is improved, and the efficient solution of altitude and heading position control commands is realized, which has practical engineering value. Attached Figure Description

[0034] Figure 1 This is a flowchart of the finite-time flight altitude control method based on integrated flap direct force control of the present invention.

[0035] Figure 2 The altitude error variation curve of the aircraft relative to the reference trajectory obtained in the example;

[0036] Figure 3 The flight heading position error variation curve obtained in the example;

[0037] Figure 4 The aircraft pitch angular velocity error variation curve obtained in the example;

[0038] Figure 5 The aircraft velocity amplitude error variation curve obtained in the example;

[0039] Figure 6 The aircraft pitch attitude angle error variation curve obtained in the example;

[0040] Figure 7 The longitudinal velocity variation curve of the aircraft obtained for the example;

[0041] Figure 8 The elevator change curve obtained for the example;

[0042] Figure 9 The curve showing the change in the aircraft flaps obtained in the example;

[0043] Figure 10 The throttle change curve of the aircraft obtained for the example. Detailed Implementation

[0044] The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0045] Example: This example calculates control commands for the finite time domain altitude adjustment problem of a certain aircraft. It is assumed that the initial state of the aircraft is cruise flight at an altitude of 1000m and a speed of 55m / s. The control objective is to increase the altitude of the aircraft by 20m within a given time of 15s, and at the same time, shift the heading position forward by 30m relative to the cruise flight at the terminal time.

[0046] For the aircraft altitude control reference trajectory, in practice, an offline trajectory from the initial point to the terminal point can be derived using optimization methods based on the aircraft's nonlinear motion equations. However, to illustrate the flexibility and convenience of the finite-time flight altitude control method based on integrated flap direct force control of this invention, the reference trajectory in this embodiment is directly taken as a cruise trajectory with an altitude of 1000m and a speed of 55m / s. Note that this reference trajectory cannot reach the target position point at the terminal moment, but this does not affect the application of the finite-time flight altitude control method based on integrated flap direct force control of this invention. The specific form of the established longitudinal channel state equation of the aircraft is as follows:

[0047] ;

[0048] in, , .

[0049] Based on the flight control objective, a finite-time linear quadratic optimal control problem is established, with the initial boundary state set as follows. , , , , , Specify the terminal boundary conditions as follows: , , , To ensure the aircraft has a forward velocity relative to the reference trajectory at the terminal moment, the terminal velocity is specified as... The terminal longitudinal velocity is free. The constructed finite-time linear quadratic optimal control problem is as follows:

[0050] ;

[0051] in, and They are Wei and A positive definite symmetric matrix , , The initial and terminal times are given as follows: and , Given an initial state value, Given a terminal state value.

[0052] In the parallel solution process using the finite-degree symplectic integration algorithm, the symplectic integration algorithm adopts the Sinhalese integration algorithm, and the discrete integration time step is taken as... According to the finite-time flight altitude control method based on integrated flap direct force control of the present invention, only 7 initial value integrations are required. The initial value guesses of the costate variables in the 7 initial value solutions are as follows: , , , , , , The corresponding coefficient calculation results are as follows , , , , , , This allows us to obtain the optimal state solution and the optimal control solution, which are then applied to the aircraft altitude control.

[0053] Figures 2-7 The state solution obtained by the finite-time flight altitude control method using the integrated flap direct force control of this invention is presented. Figures 8-10 The control solution obtained by the finite-time flight altitude control method using the integrated flap direct force control of this invention is presented. For comparison, results obtained based on the target practice method are also given. Figures 2-10 As can be seen, the solution obtained by the finite-time flight altitude control method using the integrated flap direct force control of this invention is completely consistent with the solution obtained by the target shooting method. The aircraft altitude control curve is stable, the transition is smooth, and the relative position control along the heading is ideal, reaching the desired relative position at almost constant speed. In particular, it can be seen that based on direct force flap control, the pitch attitude change of the aircraft during altitude maneuvers is very small, with a maximum change of only about 5. o The aircraft in The specified terminal altitude, heading position, angular velocity, velocity, and attitude angle boundary conditions were implemented.

[0054] Although this embodiment does not specify the longitudinal speed of the terminal, it is from... Figure 7 As can be seen, its value is very small. It can be determined that the finite-time flight altitude control method based on integrated flap direct force control of this invention is effective.

[0055] Although the embodiments of the present invention have been disclosed above, they are not limited to the applications listed in the specification and embodiments. For those skilled in the art, all features disclosed in the present invention, or all steps in all methods or processes disclosed, except for mutually exclusive features and / or steps, can be combined in any way without departing from the principles of the present invention. The present invention is not limited to the specific details and illustrations shown and described herein.

Claims

1. A finite-time flight altitude control method based on integrated flap direct force control, characterized in that, Includes the following steps: S10. Based on the background altitude control reference trajectory, establish a linearized dynamic model of the aircraft's longitudinal channel; Given a reference trajectory for aircraft altitude control, the nonlinear equations of motion of the aircraft are linearized and expanded in the vicinity of the reference trajectory. To achieve altitude control, altitude, heading position, pitch rate, velocity amplitude, pitch attitude angle, and longitudinal velocity are selected as state variables, and elevator, flaps, and engine throttle are used as control variables. The elevator provides pitch moment control, the flaps provide direct force control, and the engine throttle provides thrust control. The specific form of the established longitudinal channel state equations is as follows: ； in, For state variables, The flight altitude error of the aircraft relative to the flight altitude control reference trajectory. For heading and position error, For pitch angular velocity error, For velocity amplitude error, For pitch attitude angle error, For longitudinal velocity error, To control variables, For the change in the aircraft's elevator. Flange change amount This refers to the change in engine throttle. yes 3D matrix yes 3D matrix State variables The first derivative with respect to time, Indicates matrix transpose; S20. Based on the flight altitude control objective, establish a finite-time linear quadratic optimal control problem and derive the corresponding two-point boundary value problem; Based on the flight control objective, a finite-time linear quadratic optimal control problem is established. The dynamic transition process of state variables during aircraft altitude control is adjusted using the weight matrix in the integral performance index. Regarding the values ​​of terminal state variables, for state variables with specified terminal values, equality constraints are directly set in the finite-time linear quadratic optimal control problem; for state variables without specified terminal values, constraints are indirectly imposed using the final value performance index. Furthermore, based on optimal control theory, a two-point boundary value problem based on Hamiltonian dynamics is derived. S30. The optimal flight state control solution for flight altitude control is obtained by using a finite-order symplectic integral algorithm in parallel. For the two-point boundary value problem based on Hamiltonian dynamics, based on the principle of superposition of solutions to linear differential equations and combined with the initial conditions of state variables, a finite set of initial guesses of costate variables are given. The symplectic integral algorithm is used to solve the initial value problem in parallel within a given finite time domain to obtain the optimal flight state variable solution and costate variable solution that meet the preset conditions. Then, the corresponding optimal control solution is calculated, and the control commands for the elevator, flaps and engine throttle of the aircraft are obtained and applied to the flight altitude control of the aircraft. S40. Apply the optimal flight state control solution to the aircraft's flight altitude control.

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